Asked by GAGAN
Solve: (x-2)5^x = 5^(x+2)
Answers
Answered by
Reiny
(x-2)5^x - 5^(x+2) = 0
I see a common factor of 5^x
5^x( x-2 + 5^2) = 0
5^x(x + 23) = 0
5^x = 0 or x = -23
but 5^x = 0 has no solution, so
x = -23
I see a common factor of 5^x
5^x( x-2 + 5^2) = 0
5^x(x + 23) = 0
5^x = 0 or x = -23
but 5^x = 0 has no solution, so
x = -23
Answered by
bobpursley
take the log base 5 of each side.
log(x-2)+x =(x+2)
log(x-2)=2
log base five z=2, so x-2=25, x= 27
check it.
x-2)5^x = 5^(x+2)
25*5^25= 5^(27)
25= 5^2, checks.
log(x-2)+x =(x+2)
log(x-2)=2
log base five z=2, so x-2=25, x= 27
check it.
x-2)5^x = 5^(x+2)
25*5^25= 5^(27)
25= 5^2, checks.
Answered by
Reiny
go with bobpursley's solution
I don't know how my "-" suddenly turned into a + in my third line.
should have been:
5^x( x-2 - 5^2) = 0
5^x(x - 27) = 0
5^x = 0 or x = 27
but 5^x = 0 has no solution, so
x = 27 , the same as bob had
I don't know how my "-" suddenly turned into a + in my third line.
should have been:
5^x( x-2 - 5^2) = 0
5^x(x - 27) = 0
5^x = 0 or x = 27
but 5^x = 0 has no solution, so
x = 27 , the same as bob had
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.